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Title: Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy
Authors: Carmichael, Benoît
Koumou, Gilles Boevi
Moran, Kevin
Keywords: Portfolio Diversification
Rao's Quadratic Entropy
Diversification Return
Diversification Ratio
Portfolio Variance Normalized
Gini-Simpson Index
Markowitz's Utility Function
Bouchaud's General Free Utility
Issue Date: 2015-05
Series/Report no.: Cahiers du CIRPÉE;15-08
Abstract: This paper extends the use of Rao(1982b)’s Quadratic Entropy (RQE) to modern portfolio theory. It argues that the RQE of a portfolio is a valid, flexible and unifying approach to measuring portfolio diversification. The paper demonstrates that portfolio’s RQE can encompass most existing measures, such as the portfolio variance, the diversification ratio, the normalized portfolio variance, the diversification return or excess growth rates, the Gini-Simpson indices, the return gaps, Markowitz’s utility function and Bouchaud’s general free utility. The paper also shows that assets selected under RQE can protect portfolios from mass destruction (systemic risk) and an empirical illustration suggests that this protection is substantial.
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